Activity coefficients fractions

The activity coefficient fraction 7cr/7oH" is unity at infinite dilution, and so the value of the right-hand side of equation (50) becomes equal... 

At infinite dilution the activity coefficient fraction 7cr/7on" becomes equal to unity, so that log (7cr/7oH") is then zero under these conditions, therefore, the right-hand side of equation (45.24) becomes equal to — log Kw It follows, therefore, that if the left-hand side of this equation, for various molalities of MOH and MCI, is plotted against some function of the concentration, e.g., the ionic stren h, the intercept for infinite dilution gives the value of — log Kv, At 25° C, jB for the cell under consideration is known to be 0.2224 volt, and the actual e.m.p. of the cell, i.e., E, can be measured by assuming mcr to be equal to m2 (for MCI) and mon to be equal to Wi (for MOH), the left-hand side of equation (45.24) can be readily evaluated. From results of this kind, with various chlorides and hydroxides, Ku> has been found to be 1.008 X 10 at 25° C. Accurate measurements of the same type have been made in the temperature range from 0° to 50° C, with cells containing a number of different chlorides. 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

LIQUTD-PHASE MOLE FRACTION ACTIVITY COEFFICIENTS... 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

In thermodynamics the formal way of dealing with nonideality is to introduce an activity coefficient 7 into the relationship between activity and mole fraction ... 

The stabiHty criteria for ternary and more complex systems may be obtained from a detailed analysis involving chemical potentials (23). The activity of each component is the same in the two Hquid phases at equiHbrium, but in general the equiHbrium mole fractions are greatiy different because of the different activity coefficients. The distribution coefficient m based on mole fractions, of a consolute component C between solvents B and A can thus be expressed... 

Liquid mole fraction Vapor mole fraction Temper- ature, R Relative volatifity Pressure activity coefficient Endialpy, Btu/ (Ib-mol) Heat capacity, Btu/(lb-mol- R)... 

Consequently, the partition ratio in mole-fraction units is a result of the ratio of activity coefficients in the two layers [Eq. (15-7)]. 

Select now a second neutral indicator base C that is weaker than B by roughly an order of magnitude thus, a solvent can be found of such acidity that a significant fraction of both B and C will be protonated, but this will no longer be a dilute aqueous solution, so the individual activity coefficients will in general deviate from unity. For this solution containing low concentrations of both B and C,... 

Activity coefficients are equal to 1.0 for an ideal solution when the mole fraction is equal to the activity. The activity (a) of a component, i, at a specific temperature, pressure and composition is defined as the ratio of the fugacity of i at these conditions to the fugacity of i at the standard state [54]. 

In Chapter 7 we found it convenient to distinguish between proton transfers involving a solvent molecule and those involving only solute particles but this difference will lose its significance when the distinction between solvent and solute begins to break down. We recall that in Sec. 54 the mole fraction of the solvent did not differ appreciably from unity and could be omitted from (72). In investigating concentrated solutions, however, there is no question of extrapolating to infinite dilution the mole fraction of the solvent will differ from unity and will have to be retained in all formulas. At the same time each of the mole fractions will need to be multiplied by its activity coefficient. 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

For any component i in a liquid phase, the fugacity of f is most conveniently related to the mole fraction xt by use of the activity coefficient, y(, according to... 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

The activity coefficient is related to the mole fraction and the fugacity by... 

To determine the activity coefficient, 7r. i, one measures the melting temperature, T, of a solution with mole fraction,. V], and calculates a from equation (6.166). The activity coefficient is then obtained from... 

The thermodynamic activity equilibrium constant (Ka) is expressed in terms of mole fraction (X) and activity coefficient (y) by the following equation ... 

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